TY - JOUR
T1 - Fast Numerical Solvers for Subdiffusion Problems with Spatial Interfaces
AU - Yu , Boyang
AU - Li , Yonghai
AU - Liu , Jiangguo
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 431
EP - 458
PY - 2024
DA - 2024/05
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1017
UR - https://global-sci.org/intro/article_detail/ijnam/23130.html
KW - Caputo and Riemann-Liouville derivatives, fast numerical solvers, fractional order fluxes, interface problems, subdiffusion, sum of exponentials (SOE).
AB - <p style="text-align: justify;">This paper develops novel fast numerical solvers for subdiffusion problems with spatial interfaces. These problems are modeled by partial differential equations that contain both
fractional order and conventional first order time derivatives. The former is non-local and approximated by L1 and L2 discretizations along with fast evaluation algorithms based on approximation
by sums of exponentials. This results in an effective treatment of the “long-tail” kernel of subdiffusion. The latter is local and hence conventional implicit Euler or Crank-Nicolson discretizations
can be used. Finite volumes are utilized for spatial discretization based on consideration of local
mass conservation. Interface conditions for mass and fractional fluxes are incorporated into these
fast solvers. Computational complexity and implementation procedures are briefly discussed.
Numerical experiments demonstrate accuracy and efficiency of these new fast solvers.</p>